Question

Question 45

Fill in the blanks to make the statements true.

The least number by which 125 be multiplied to make it a perfect square is ___.

Answer 1

5
Resolving 125 into prime factors, we get
$\begin{array}{cc}5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$125=5\times 5\times 5$
Grouping the factors in doublet of equal factors, we get
$125=(5\times 5)\times 5$
We observe that 5 is without a pair.
Thus, we must multiply the number by 5, so that the product is a perfect square.
Hence, the least number, which should be multiplied by 125 to make it a perfect square is 5.